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A221401
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Number of 2 X n arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, with no 2-loops and with no occupancy greater than 2.
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1
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0, 1, 6, 56, 324, 2196, 13328, 83680, 512752, 3161248, 19384848, 118981520, 729388016, 4471790032, 27407876144, 167983235088, 1029494729904, 6309251897744, 38665450224432, 236955187985936, 1452135101851056
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 7*a(n-1) + 6*a(n-2) - 74*a(n-3) + 8*a(n-4) + 132*a(n-5) - 72*a(n-6) - 24*a(n-7) + 16*a(n-8).
Empirical g.f.: x^2*(1 - 2*x)*(1 + x + 10*x^2 - 10*x^3 + 8*x^4 - 8*x^5) / ((1 - 4*x + 2*x^2)*(1 + 2*x - 2*x^2)*(1 - 5*x - 8*x^2 + 6*x^3 + 4*x^4)). - Colin Barker, Aug 05 2018
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EXAMPLE
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All solutions for n=3:
..0..2..1....1..2..1....0..2..0....0..2..1....1..2..0....1..2..0
..0..2..1....0..2..0....1..2..1....1..2..0....1..2..0....0..2..1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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